He said: "The fact that the Office for National Statistics is going to look at these different sources and reconcile them is entirely welcome.

"This is an important issue, we know the current numbers are far from perfect and the Government has data which is highly relevant. They are doing their best to hide it from us."

Official figures suggest that 257,000 EU migrants came to Britain last year, but over the same period 630,000 EU citizens registered for a national insurance number.

David Cameron has refused a request to release the figures, claiming that the difference is accounted for by short term migrants.

Official migration figures are based on a survey of more than 800,000 migrants as they enter and leave Britain, known as the International Passenger Survey.

The ONS said that "at times when migration patterns change significantly, there is a risk that the International Passenger Survey design may need to be changed to fit these".

Immigration is growing, but where has everyone been coming from? Photo: ALAMY

It said: "When available, DWP and HMRC data on national insurance number activity (those who have applied for a national insurance number and are still active in the UK) will be incorporated to provide additional information for the users of our statistics and a more complete picture."

Earlier this month John Whittingdale, the Culture Secretary, told The Daily Telegraph: "There is already enormous concern on the basis of the numbers that that are published. The suggestion that they may understate the position is a cause for even greater concern.

"I have heard the reasons why national insurance numbers don't necessarily reflect actual levels but at the very least that's a debate which we need to have and I can see no reason why we can't have the figures.

"The massive influx that has occurred as a result particularly of the expansion of the EU is putting pressure on all of the public services - housing, education, health.

"It is creaking at he seams. There is a very strong feeling that his is a small country and we simply cannot go on having an enormous influx over which we have no control."

Passports are to be checked upon leaving the United Kingdom Photo: Andy Rain/EPA